SparseTSCGM (version 1.0)

sparse.tscgm: Sparse time series chain graphical models

Description

Computes sparse autoregressive coefficients matrix and precision matrix estimates for time series chain graphical models using SCAD penalty. In time series chain graphical models directed edges or links are identified by nonzero entries of the autoregressive coefficients matrix and undirected edges or links are identified by nonzero entries of the precision matrix.

Usage

sparse.tscgm(data=data, lam1 = lam1, lam2 = lam2, B.start = NULL, 
     model.select = c("null", "bic"), maxit.out = 100,  maxit.in = 500, 
     tol.out = 1e-04, tol.in = 1e-05, tol = 1e-05, silent = TRUE)

Arguments

data

Longitudinal data format.

lam1

Either a scalar or a vector of tuning parameter values for the SCAD penalty on the precision matrix. If lam1 is a vector with length at least 2, minimum BIC will be performed to select the optimal tuning parameter.

lam2

Either a scalar or a vector of tuning parameter values for the SCAD penalty on the autoregression matrix. If lam2 is a vector with length at least 2, minimum BIC will be performed to select the optimal tuning parameter

B.start

The user can optionally specify a starting value for the autoregresive coefficients matrix.

model.select

model.select="null" computes the time series chain graphical model solutions using specified scalar values of the tuning parameters lam1 and lam2, model.select="bic" first selects the optimal SCAD

maxit.out

The maximum allowable outer iterations of the algorithm. The outer-loop iterates alternatively to estimate the precision matrix and the autoregression matrix until convergence.

maxit.in

The maximum allowable iterations of the algorithm that minimizes with respect to the autoregression coefficient matrix.

tol.out

Convergence tolerance for outer-loop of the algorithm that alternate between the estimation of precision matrix and autoregressive coefficients matrix.

tol.in

Convergence tolerance for inner-loop of the algorithm that minimizes with respect to the autoregression coefficient matrix.

tol

Convergence tolerance for the algorithm that minimizes with respect to the autoregressive coefficients matrix.

silent

Either TRUE or FALSE. If silent=FALSE this function will display progress updates to the screen.

Value

• A list containing:
• Bhat
  Autoregressive coefficients matrix estimate. The nonzero estimates of the autoregression matrix can be used to represent directed edges or links for chain graphical modeling.
• omega
  Precision matrix estimate. The nonzero estimates of the precision matrix can be used to represent undirected edges or links for chain graphical modeling.
• lambda1
  The optimal tuinng parameter for the SCAD penalty on the precision matrix selected with minimum BIC criterion. If tuning parameter selection using BIC is not performed, lambda1 will be NULL
• .
• lambda2
  The optimal tuinng parameter for the SCAD penalty on the autoregressive coefficients matrix selected with minimum BIC criterion. If tuning parameter selection using BIC is not performed, lambda2 will be NULL.

Details

For description of the objective functions see Abegaz and Wit (2012).

References

Fentaw Abegaz and Ernst wit (2012) Sparse time series chain graphical models for reconstructing genetic networks. Biostatistics, doi:10.1093/biostatistics/kxt005. Rothman, A.J., Levina, E., and Zhu, J. (2010) Sparse multivariate regression with covariance estimation. Journal of Computational and Graphical Statistics. 19: 947--962.

Examples

#Simulated data from random graph
set.seed(1)
simu <- sim.data(time=10,n_obs=5, n_var=20,prob0=0.15)
Sdata <- simu$data1

lam1=0.43
lam2=0.27

res.tscgm <- sparse.tscgm(data=Sdata, lam1=lam1, lam2=lam2, B.start = NULL, 
              model.select="null", maxit.out = 100, maxit.in = 500, 
             tol.out = 1e-04, tol.in = 1e-05, silent = TRUE) 
B <- res.tscgm$Bhat
om <- res.tscgm$omega

### Plot chain graph

  ### plot of undirected graph 
  
colnames(om) <-  rownames(om) <- colnames(Sdata)
network_precm <- network(om)
plot.network(network_precm,label = network.vertex.names(network_precm),
  usearrows = FALSE, displayisolates = FALSE, pad = 0.01,label.pad = 0.3, 
  label.col = 6, vertex.col = 5,vertex.cex = 1.5,
  edge.col = 4, mode = "fruchtermanreingold", interactive=FALSE)

   ### Plot of directed graph
 
colnames(B) <-  rownames(B) <- colnames(Sdata)
network.autoregm <- network(B)
plot.network(network.autoregm,label = network.vertex.names(network.autoregm),
  usearrows = TRUE, displayisolates = FALSE, pad = 0.01,label.pad = 0.3, 
  label.col = 6, vertex.col = 5,vertex.cex = 1.5,
  edge.col = 3, mode = "fruchtermanreingold", interactive=FALSE)